RU2509346C1 - Method of monitoring dead-end situations in information and communication system and apparatus for realising said method - Google Patents

Abstract

FIELD: information technology.

SUBSTANCE: method of monitoring dead-end situations in an information and communication system involves determining the values: $${\lambda }_{r_{it}}$$

- mathematical expectation of failure rate of the i-th critical technical resource r_it, where i=1, 2, 3, …, $$h_{r_{jp}}$$

- mathematical expectation of failure rate of the j-th critical software resource r_jp, where j=1, 2, 3,…, of the size q of the buffer memory zone of a unit of the information and communication system; setting t_tis - the time interval for scheduled execution of processes and calculating the value of the readiness factor K_rr using the formula: $$K_{rr}={\displaystyle \prod }_{i=1}^{rit}e{}^{-\lambda r_{it}{t}_{tis}}\times {\displaystyle \prod }_{j=1}^{rjp}{e}^{-h{r}_{jp}{t}_{tis}}\times {\displaystyle \prod }_{n=1}^N{e}^{-k{@}_e{q}_n}{\displaystyle \sum }_{i=1}^{k-1}\frac{{\left(k{@}_e{q}_n\right)}^i}{i!},$$

where: i=1, 2, 3, …, is the number of critical resources r_it; j=1, 2, 3,…, is the number of critical software resources i_jp; $${\lambda }_{r_{it}}$$

mathematical expectation of failure rate of the 1-th critical technical resource r_it; t_tis is the time interval for scheduled execution of processes; $$h_{r_{jp}}$$

is the mathematical expectation of failure rate of the j-th critical software resource r_jp; k is the order of the approximating Erlang distribution with parameter @_e - Poisson intensity in the unit for an integer value of the size q of the buffer memory zone of the unit of the information and communication system; N is the total number of buffer memory zones in the information and communication system; q is the size of the buffer memory zone of the unit of the information and communication system; comparing the determined readiness factor K_rr with a threshold level K_{rr (0)} and if the condition K_rr < K_{rr (0)} is satisfied, there are dead-end situations in the information and communication system.

EFFECT: high efficiency of determining dead-end situations, especially if there are multiple different-type resources, with incomplete a priori information on resources required by the processes, taking into account attributes of critical resources - reliability factors of technical and software resources and sizes of the buffer memory of units of the information and communication system.

2 cl, 2 dwg

Description

The invention relates to the field of monitoring deadlocks in automation, communication and computer systems (info-communications), mainly in space rocket technology, in the space and ground control segments.

The term “infocommunication technologies” includes: information technologies (hardware and software), telecommunication equipment (subscriber equipment, network equipment) and telecommunication services (services in public telephone networks, Internet services, mobile phone services, etc. ) Infocommunication technologies are implemented using infocommunication networks. According to the law “On Information ...” an infocommunication network is a technological system designed to transmit information via communication lines, access to which is carried out using computer equipment (for more details, see the website with a list of references - (D1)).

The growing demand for infocommunication services is explained by the need of society for sustainable remote communications, which allow organizing new forms of production and management of real and virtual enterprises and organizations. It is in this direction that the Department of State Policy in the Field of Infocommunication Technologies of the Ministry of Information Technologies and Communications of the Russian Federation conducts its work (see the report of the Acting Director of the Department of State Policy in the Field of Infocommunication Technologies E.S. Vasilyeva "State Policy in the Field of Infocommunication Technologies ", The site _mis_2008 Vasiliev.htm - (D2)).

In the real world, the functioning of infocommunication systems is constantly affected by such destabilizing factors as failures, failures, software errors, violations of synchronization systems, imperfect architectural and design solutions, conflicts, deadlocks, emergency and fan blackouts, viruses, and hacker attacks , "Spam", etc. The materials of this application consider deadlock situations (hereinafter referred to as deadlocks) arising from the use of a common set of resources, the so-called critical resources. A resource is understood to be any component of the system (technical, software, information) that has its own unique name or address and is allocated to processes for temporary use. Moreover, the use of resources can be either exclusive or shared by many processes.

Deadlocks are situations of mutual expectation by two or more processes simultaneously executing in the system of releasing the same set of critical resources occupied by other processes. In this case, these processes are not performed in the system, and when all elements are operational, the system does not fulfill the functions assigned to it and is in a standby state. Administrator intervention is required to forcibly release the aggregate of critical resources and break the deadlock by activating the execution of processes that have reached the deadlock (for more details see the article by V. Kozlov, “Extended Classification of Dead Ends,” VKSS Connect! Magazine, No. 4, 2005 - (D3 )).

A number of methods are known for controlling deadlocks, which are the basis for the so-called prevention of deadlocks while simultaneously executing several software processes. The most common should include methods of interrupting the processes described in Trachtengerz E.A. "Software for parallel processes." M., Science, 1987, 272 p. - (D4), Dijkstra E. “Interaction of sequential processes, in the book. Programming Languages ”, M., Mir, 1972, pp. 3-86 - (D5), Haberman A.N. Prevention of System deadlocks. - Communications ACM, 1969, vol.12, N 7, p.373-377 - (D6) and in patent RU No. 2287220 "System and method for preventing deadlocks using a timer for high-speed downlink packet access", published 2006.11.10 - (D 7)).

The method of interrupting the process (D4) is based on the following sequence of actions. The execution of a process that requested some system resources occupied at the time of the request is interrupted and all resources it owned are taken from it. After releasing the required resources by other processes, the interrupted process is again activated until the next request for the occupied resources.

The disadvantage of this method is that it is specific and ineffective, especially in the case of the presence of many heterogeneous resources that are requested dynamically, it requires frequent removal of processes, which leads to unproductive time costs.

The method (D5), also known as the banker's algorithm, contains actions for analyzing the ratio of the number of requested resources to the number of free, that is, those whose allocation does not allow dead-end states of the system. In accordance with this, the process is denied access to free resources, the allocation of which will lead to a dead end. The main disadvantages of this method are: limited scope, since it works with resources of the same type of non-unit capacity, the requirement for complete a priori information about the resources required for the processes.

The method (D6) is based on the same idea as in the method (D5), however, it is applicable to systems with heterogeneous resources of unit capacity and is based on the forecasting of dead ends. The disadvantages include: the inability to have complete a priori information when subscribers work interactively, when processes dynamically request resources upon their requests, the need to constantly monitor the status of resources for each request from any of the processes, which affects the efficiency of the system.

The main common drawback of this group of methods to prevent, including the use of a timer (D7), should be attributed to their inability to protect against architectural deadlocks caused by attributes of critical resources such as reliability indicators of technical, software resources and buffer sizes of system nodes ( D3).

Closest to the achieved result to the claimed invention (both to a method and to a device) is the technical solution described in USSR author's certificate No. 1180890 "Device for detecting deadlocks when servicing requests for computer system resources", published on 09/23/1985. - (D8). Note that the specified well-known technical solution has the same purpose as stated - the identification or control of deadlocks and therefore selected as a prototype. The prototype is characterized by the following features. A device for detecting deadlocks when servicing requests for resources of a computing system containing a memory register, an output OR element, and M situation assessment units (M is the number of processes being serviced), each of which contains first and second registers, an AND element, an OR element, five groups OR elements and two groups of AND elements, the first group of AND elements and the first group of OR elements of the i-th situation assessment unit (1, ..., M) consist of j subgroups (j is the number of alternative combinations of resources required by the i-th process) by n items in each subgroup (n is the number of distributed resources), the outputs of even bits of the first register are connected respectively to the first inputs of the elements of the first group, the second inputs of the Jx elements of all the subgroups of the first group (j = 1, n) are connected to the output of the jth element OR the second groups, outputs of elements and the Kth subgroup of the first group (K = 1, j) are connected respectively to the inputs of the Kth element OR of the third group, the bit outputs of the second register are connected respectively to the first inputs of the elements AND of the second group, the second inputs of which are combined and connected to the output of the OR element, the first inputs of the OR elements of all the situation assessment blocks are combined and are the installation input of the device, the outputs of the AND elements of all situation assessment blocks are connected respectively to the inputs of the OR output element, the output of the i-th element of the second group is connected to the first inputs of the OR elements of the fourth and fifth group, characterized in that in order to expand functionality by identifying deadlocks with an alternative request for collective and individual resources, the j-th output the memory track is connected to the first input of the jth OR element of each subgroup of the first group in each situation assessment block and is the jth information output of the device, and in each situation assessment block, the odd-digit outputs of the first register are connected respectively to the second inputs of the OR elements of the first group, the outputs of which are connected respectively to the third inputs of the AND elements of the first group, the outputs of the OR elements of the third group are connected respectively to the inputs of the AND element, the output of which is connected to the second move of the OR element, output j the fifth group of OR j-th situation assessment block (j = 1, M = 1) coupled to the first input of the j-th element or the second group. The disadvantages of the known technical solution include its inefficiency, especially in the event of architectural-type deadlocks caused by a multitude of critical resources of various types with attributes such as reliability indicators of technical and software resources and buffer sizes of system nodes.

как функцию от таких атрибутов, как интенсивность отказов критических технических и программных ресурсов, размеры зон буферной памяти узлов инфокоммуникационной системы (ИКС). В свою очередь, через вероятность возникновения тупика Р $${}_{туп}$$

определяется коэффициент готовности ИКС, по значению которого судят о наличии тупиковых ситуаций (см. Приложение).The technical result of the invention is to increase efficiency, especially in the case of the presence of many heterogeneous resources of the infocommunication system, with incomplete a priori information about the resources required for the processes, taking into account the reliability indicators of technical, software resources and the size of the buffer memory of the system nodes. So, using the matrix method, the composition of critical resources * R is determined as the numbers of nonzero columns. Having a set of critical resources * R, due to which a deadlock is possible, it is easy to obtain an analytical expression of the probability of a deadlock R $${}_{t\mathrm{at}P}$$

as a function of such attributes as the failure rate of critical technical and software resources, the size of the buffer memory zones of the nodes of the infocommunication system (ICS). In turn, through the probability of a deadlock P $${}_{t\mathrm{at}P}$$

the ICS readiness coefficient is determined, by the value of which they judge the presence of deadlocks (see Appendix).

- математического ожидания интенсивности отказов i-гo критического технического ресурса r_iт, где i=1,2,3,…, $$h_{r_{jп}}$$

- математического ожидания интенсивности отказов j-гo критического программного ресурса r_jп, где j=1, 2, 3,…, размера q зоны буферной памяти узла инфокоммуникационной системы, задают t_внп - значение временного интервала планируемого выполнения процессов и вычисляют значение коэффициента готовности - К_гтр по формуле:The specified technical result is achieved by the fact that in the claimed method of monitoring deadlocks of the infocommunication system (ICS), the values are determined: $${\lambda }_{r_{it}}$$

- the mathematical expectation of the failure rate of the i-th critical technical resource r _it , where i = 1,2,3, ..., $$h_{r_{jP}}$$

- the mathematical expectation of the failure rate of the j-th critical software resource r _jп , where j = 1, 2, 3, ..., the size q of the buffer memory zone of the infocommunication system node, set t _vnp is the value of the time interval of the planned process execution and the readiness coefficient is calculated - K _gt according to the formula:

$${\mathrm{TO}}_{gtR}={\displaystyle \prod }_{i=\mathrm{one}}^{r_{it}}e{}^{-\lambda r_{it}{t}_{\mathrm{at}nP}}\times {\displaystyle \prod }_{j=\mathrm{one}}^{r_{jP}}{e}^{-h{r}_{jP}{t}_{\mathrm{at}nP}}\times {\displaystyle \prod }_{n=\mathrm{one}}^N{e}^{-k{@}_{\mathrm{uh}}{q}_n}{\displaystyle \sum }_{i=\mathrm{one}}^{k-\mathrm{one}}\frac{{\left(k{@}_{\mathrm{uh}}{q}_n\right)}^i}{i!}$$

where i = 1,2,3, ..., is the number of critical technical resources r _it ;

j = 1,2,3, ..., is the number of critical software resources r _jп ;

- математическое ожидание интенсивности отказов i-гo критического технического ресурса r_iт; $${\lambda }_{r_{it}}$$

- the mathematical expectation of the failure rate of the i-th critical technical resource r _i ;

t _vnp - the time interval of the planned execution of processes;

- математическое ожидание интенсивности отказов j-гo критического программного ресурса r_jп; $$h_{r_{jP}}$$

- the mathematical expectation of the failure rate j-th critical software resource r _jп ;

k is the order of the approximating Erlang distribution with the parameter @ _e - the intensity of the Poisson stream to the node for an integer value of the size q of the buffer zone of the node of the infocommunication system;

N is the total number of buffer memory zones in the infocommunication system;

q is the size of the buffer memory area of the infocommunication system node,

compare a certain availability factor - K _gtr with a threshold level of K _{gtr (0)} and when the condition is met:

K _gtr <K _{gtr (0)}

conclude that there are deadlocks in the infocommunication system.

- математического ожидания интенсивности отказов i-гo критического технического ресурса r_iт, $$h_{r_{jп}}$$

- математического ожидания интенсивности отказов j-гo критического программного ресурса r_jп, размера q зоны буферной памяти инфокоммуникационной узла системы осуществляют теоретически или эмпирически или выбирают из баз данных, например, в системе технической эксплуатации сетей связи с помощью подсистем контроля и измерений осуществляют реализацию задач управления качеством с целью оценки таких же показателей и параметров используемых средств системы, см. «Системы управления сетями связи»: учебное пособие. /М.М.Егунов, О.Г.Шерстнева, Е.А.Абзапарова - Екатеринбург: УрТИСИ ГОУ ВПО «СибГУТИ», 2009. - раздел 1.2 - [Д9]. Значение t_внп - временного интервала планируемого выполнения процессов задают как исходные данные.In this case, the definition of values: $${\lambda }_{r_{it}}$$

- the mathematical expectation of the failure rate of the i-th critical technical resource r _i $$h_{r_{jP}}$$

- the mathematical expectation of the failure rate of the jth critical program resource r _jp , the size q of the buffer memory zone of the system’s infocommunication node is carried out theoretically or empirically or selected from databases, for example, in the technical operation system of communication networks using control and measurement subsystems, control tasks are carried out quality in order to assess the same indicators and parameters of the used system tools, see "Communication Network Management Systems": a training manual. / M.M. Egunov, OG Sherstneva, E. A. Abzaparova - Yekaterinburg: UrTISI GOU VPO SibGUTI, 2009. - Section 1.2 - [D9]. The value of t _vnp - the time interval of the planned process execution is set as the source data.

The claimed method of monitoring deadlocks of the infocommunication system and device for its implementation are illustrated by the following figures:

figure 1 presents a structural diagram of a device for monitoring deadlocks of infocommunication systems,

_figure 2 presents the algorithm for calculating the value of the availability factor - K _gtr .

The deadlock control device for infocommunication systems contains:

- математического ожидания интенсивности отказов i-гo критического технического ресурса r_iт,1 - forming unit $${\lambda }_{r_{it}}$$

- the mathematical expectation of the failure rate of the i-th critical technical resource r _i

интенсивности отказов j-гo критического программного ресурса r_jп,2 - block the formation of mathematical expectation $$h_{r_{jP}}$$

the failure rate of the jth critical software resource r _jp ,

3 - block forming the size of the q zone of the buffer memory node of the infocommunication system,

4 - block formation t _GNP - time interval of the planned execution of processes,

5 - block calculating the value of the coefficient of readiness K _gtr ,

6 - comparison unit,

7 - block threshold level.

- математического ожидания интенсивности отказов i-го критического программного ресурса r_iт, блок формирования $$h_{r_{jп}}$$

- математического ожидания интенсивности отказов j-гo критического программного ресурса r_jп, блок формирования размера q зоны буферной памяти узла инфокоммуникационной системы и блок формирования t_внп - временного интервала планируемого выполнения процессов, выходы которых соответственно подключены к первому, второму, третьему и четвертому входу блока вычисления значения коэффициента готовности, выход которого соединен с первым входом блока сравнения, второй вход которого подключен к выходу блока задания порогового уровня, при этом блок вычисления значения коэффициента готовности реализует вычисление по формуле:The technical result is achieved by the fact that the device for monitoring deadlocks of the infocommunication system contains a forming unit $${\lambda }_{r_{it}}$$

- the mathematical expectation of the failure rate of the i-th critical software resource r _it , formation unit $$h_{r_{jP}}$$

- the mathematical expectation of the failure rate of the j-th critical software resource r _jп , the block for forming the size q of the buffer memory zone of the infocommunication system node and the unit for generating t _tnp - the time interval of the planned execution of the processes, the outputs of which are respectively connected to the first, second, third and fourth input of the block calculating the value of the availability factor, the output of which is connected to the first input of the comparison unit, the second input of which is connected to the output of the threshold level setting unit, while approx value calculating implements availability factor calculation according to the formula:

$${\mathrm{TO}}_{gtR}={\displaystyle \prod }_{i=\mathrm{one}}^{r_{it}}e{}^{-\lambda r_{it}{t}_{\mathrm{at}nP}}\times {\displaystyle \prod }_{j=\mathrm{one}}^{r_{jP}}{e}^{-h{r}_{jP}{t}_{\mathrm{at}nP}}\times {\displaystyle \prod }_{n=\mathrm{one}}^N{e}^{-k{@}_{\mathrm{uh}}{q}_n}{\displaystyle \sum }_{i=\mathrm{one}}^{k-\mathrm{one}}\frac{{\left(k{@}_{\mathrm{uh}}{q}_n\right)}^i}{i!}$$

where i = 1,2,3, ..., is the number of critical technical resources r _it ;

j = 1,2, 3, ..., is the number of critical software resources r _jп ;

- математическое ожидание интенсивности отказов i-гo критического технического ресурса r_iт; $${\lambda }_{r_{it}}$$

- the mathematical expectation of the failure rate of the i-th critical technical resource r _i ;

t _vnp - the time interval of the planned execution of processes;

- математическое ожидание интенсивности отказов j-гo критического программного ресурса r_jп; $$h_{r_{jP}}$$

- the mathematical expectation of the failure rate j-th critical software resource r _jп ;

k is the order of the approximating Erlang distribution with the parameter @ _e - the intensity of the Poisson stream to the node for an integer value of the size q of the buffer zone of the node of the infocommunication system;

N is the total number of buffer memory zones in the infocommunication system;

q is the size of the buffer memory area of the infocommunication system node,

and the output of the comparison unit is the output of the deadlock control device of the infocommunication system.

- математического ожидания интенсивности отказов i-го критического технического ресурса r_iт 1, формирования $$h_{r_{jп}}$$

- математического ожидания интенсивности отказов j-гo критического программного ресурса r_jп 2, формирования размера q зоны буферной памяти узла инфокоммуникационной системы и формирования t_внп - временного интервала планируемого выполнения процессов 4 вводят числовые значения $${\lambda }_{r_{iт}}$$

- математического ожидания интенсивности отказов i-гo критического технического ресурса r_iт, $$h_{r_{jп}}$$

- математического ожидания интенсивности отказов j-гo критического программного ресурса r_jп, размера q зоны буферной памяти узла инфокоммуникационной системы и t_внп - временного интервала планируемого выполнения процессов, которые поступают соответственно на первый, второй, третий и четвертый входы блока вычисления значения коэффициента готовности К_гтр 5. Блок вычисления значения коэффициента готовности К_гтр 5 реализует вычисление по формуле:The device operates as follows. In the formation blocks $${\lambda }_{r_{it}}$$

- the mathematical expectation of the failure rate of the i-th critical technical resource r _i 1, formation $$h_{r_{jP}}$$

- the mathematical expectation of the failure rate of the j-th critical software resource r _jп 2, the formation of the size q of the buffer memory zone of the infocommunication system node and the formation of t _tnp - the time interval of the planned process 4, enter numerical values $${\lambda }_{r_{it}}$$

- the mathematical expectation of the failure rate of the i-th critical technical resource r _i $$h_{r_{jP}}$$

- the mathematical expectation of the failure rate of the jth critical program resource r _jp , the size q of the buffer memory zone of the infocommunication system node, and t _GNP - the time interval of the planned execution of the processes that arrive at the first, second, third, and fourth inputs of the unit for calculating the readiness coefficient K _gtr 5. The unit for calculating the value of the availability factor K _gtr 5 implements the calculation by the formula:

$${\mathrm{TO}}_{gtR}={\displaystyle \prod }_{i=\mathrm{one}}^{r_{it}}e{}^{-\lambda r_{it}{t}_{\mathrm{at}nP}}\times {\displaystyle \prod }_{j=\mathrm{one}}^{r_{jP}}{e}^{-h{r}_{jP}{t}_{\mathrm{at}nP}}\times {\displaystyle \prod }_{n=\mathrm{one}}^N{e}^{-k{@}_{\mathrm{uh}}{q}_n}{\displaystyle \sum }_{i=\mathrm{one}}^{k-\mathrm{one}}\frac{{\left(k{@}_{\mathrm{uh}}{q}_n\right)}^i}{i!}$$

Where

i = 1,2,3, ..., is the number of critical technical resources r _it ;

j = l, 2,3, ..., is the number of critical software resources r _jп ;

- математическое ожидание интенсивности отказов i-го критического технического ресурса r_iт; $${\lambda }_{r_{it}}$$

- the mathematical expectation of the failure rate of the i-th critical technical resource r _i ;

t _vnp - the time interval of the planned execution of processes;

- математическое ожидание интенсивности отказов j-гo критического программного ресурса r_jп; $$h_{r_{jP}}$$

- the mathematical expectation of the failure rate j-th critical software resource r _jп ;

k is the order of the approximating Erlang distribution with the parameter @ _e - the intensity of the Poisson stream to the node for an integer value of the size q of the buffer zone of the node of the infocommunication system;

N is the total number of buffer memory zones in the infocommunication system;

q is the size of the buffer memory area of the infocommunication system node,

The calculated value of K _{gtr is} supplied to the first input of the comparison unit 6, the second input of which from the output of the task unit of the threshold level 7 receives the threshold level K _{gtr (0)} and when the condition is met:

K _gtr <K _{gtr (0)}

at the output of the comparison unit 6, a signal appears, for example, a high-level potential, which indicates the presence of deadlocks in the infocommunication system.

We show the possibility of carrying out the invention, i.e. the possibility of its industrial application.

- математического ожидания интенсивности отказов i-го критического технического ресурса r_iт, h $${}_{r_{jп}}$$

- математического ожидания интенсивности отказов j-гo критического программного ресурса r_jп, размера q зоны буферной памяти узла инфокоммуникационной системы и t_внп - временного интервала планируемого выполнения процессов соответственно. Они известны и широко применяются в различных областях. Это различные клавиатуры и устройства ввода для компьютеров, для калькуляторов, для введения исходных данных в различные системы, например в часы.The formation blocks 1-4, made with the possibility of recording numerical values in them, are intended to record numerical values in them: λ $${}_{r_{it}}$$

- the mathematical expectation of the failure rate of the i-th critical technical resource r _it , h $${}_{r_{jP}}$$

- the mathematical expectation of the failure rate of the jth critical program resource r _jp , the size q of the buffer memory area of the infocommunication system node, and t _vnp - the time interval of the planned process execution, respectively. They are known and widely used in various fields. These are various keyboards and input devices for computers, for calculators, for inputting input data into various systems, for example, in watches.

The calculation unit 5, which provides the calculation of the readiness coefficient K _gtr , is characterized in the application materials at the functional level, and its implementation involves the use of programmable tools, while the application materials show the corresponding calculated mathematical expression, and figure 2 shows a computational algorithm in the form of a block -scheme. Such programmable tools are known: microprocessor, personal computer, computers, see, for example, information sources: Pyatibratov A.P., Gudyno L.P. Kirichenko A.A. "Computing systems, networks and communications." - M.: Finance and Statistics, 2004, p.1-273 - (D10), Pool L. “Work on a personal computer”: Per. from English - M .: Mir, 1986, p. 73-88 (D11).

Comparison unit 6 is configured to compare two numerical values and provide a signal when one is exceeded over the other. Electronic circuits that perform this function are called comparators. They are known, see, for example, "Analog and digital integrated circuits." Directory. Yakubovsky S.V., Kuleshova V.I., Nisselson L.I. et al., ed. Yakubovskogo S.V., M, Radio and Communications, 495 pages (D12), which contains a description of the 564IP2 chip, designed to compare two four-digit binary numbers.

A block for setting the threshold level 7 is also known, which is configured to record a numerical value into it and is equivalent to the blocks 1-4 described earlier.

Claims (2)

1. The way to control the deadlocks of the infocommunication system, which consists in determining the values: $${\lambda }_{r_{it}}$$

- the mathematical expectation of the failure rate of the i-th critical technical resource r _it , where i = 1, 2, 3, ..., $$h_{r_{jP}}$$

- the mathematical expectation of the failure rate of the j-th critical software resource r _jп , where j = 1, 2, 3, ..., the size q of the buffer memory zone of the infocommunication system node, set t _vnp is the value of the time interval of the planned process execution and the readiness coefficient is calculated - K _gt according to the formula:
$${\mathrm{TO}}_{gtR}={\displaystyle \prod }_{i=\mathrm{one}}^{r_{it}}e{}^{-\lambda r_{it}{t}_{\mathrm{at}nP}}\times {\displaystyle \prod }_{j=\mathrm{one}}^{r_{jP}}{e}^{-h{r}_{jP}{t}_{\mathrm{at}nP}}\times {\displaystyle \prod }_{n=\mathrm{one}}^N{e}^{-k{@}_{\mathrm{uh}}{q}_n}{\displaystyle \sum }_{i=\mathrm{one}}^{k-\mathrm{one}}\frac{{\left(k{@}_{\mathrm{uh}}{q}_n\right)}^i}{i!}$$

Where
i = 1,2,3, ..., is the number of critical technical resources r _it ;
j = 1,2,3, ..., is the number of critical software resources r _jп ;
$${\lambda }_{r_{it}}$$

- the mathematical expectation of the failure rate of the i-th critical technical resource r _i ;
t _vnp - the time interval of the planned execution of processes;
$$h_{r_{jP}}$$

- the mathematical expectation of the failure rate j-th critical software resource r _jп ;
k is the order of the approximating Erlang distribution with the parameter @ _e - the intensity of the Poisson stream to the node for an integer value of the size q of the buffer zone of the node of the infocommunication system;
N is the total number of buffer memory zones in the infocommunication system;
q is the size of the buffer memory area of the infocommunication system node,
compare a certain availability factor - K _gtr with a threshold level of K _{gtr (0)} and when the condition is met:
K _gtr <K _{gtr (0)}
conclude that there is a deadlock in the infocommunication system. 2. A device for monitoring deadlocks of an infocommunication system, comprising a formation unit $${\lambda }_{r_{it}}$$

- the mathematical expectation of the failure rate of the i-th critical technical resource r _it , where i = 1, 2, 3, ..., the formation unit $$h_{r_{jP}}$$

- the mathematical expectation of the failure rate of the j-th critical software resource r _jп , where j = 1, 2, 3, ..., the block for forming the size q of the buffer memory zone of the infocommunication system node and the block for generating t _tnp - the time interval of the planned execution of processes whose outputs are respectively connected to the first, second, third and fourth input of the unit for calculating the readiness coefficient value, the output of which is connected to the first input of the comparison unit, the second input of which is connected to the output of the threshold level setting unit , The value calculation unit availability factor K _GAD implementing calculation according to the formula:
$${\mathrm{TO}}_{gtR}={\displaystyle \prod }_{i=\mathrm{one}}^{r_{it}}e{}^{-\lambda r_{it}{t}_{\mathrm{at}nP}}\times {\displaystyle \prod }_{j=\mathrm{one}}^{r_{jP}}{e}^{-h{r}_{jP}{t}_{\mathrm{at}nP}}\times {\displaystyle \prod }_{n=\mathrm{one}}^N{e}^{-k{@}_{\mathrm{uh}}{q}_n}{\displaystyle \sum }_{i=\mathrm{one}}^{k-\mathrm{one}}\frac{{\left(k{@}_{\mathrm{uh}}{q}_n\right)}^i}{i!}$$

Where
i = 1,2,3, ..., is the number of critical technical resources r _it ;
j = 1,2,3, ..., is the number of critical software resources r _jп ;
$${\lambda }_{r_{it}}$$

- the mathematical expectation of the failure rate of the i-th critical technical resource r _i ;
t _vnp - the time interval of the planned execution of processes;
$$h_{r_{jP}}$$

- the mathematical expectation of the failure rate j-th critical software resource r _jп ;
k is the order of the approximating Erlang distribution with the parameter @ _e - the intensity of the Poisson stream to the node for an integer value of the size q of the buffer zone of the node of the infocommunication system;
N is the total number of buffer memory zones in the infocommunication system;
q is the size of the buffer memory area of the infocommunication system node,
and the output of the comparison unit is the output of the deadlock control device of the infocommunication system.

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